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Author
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Topic: Questions on Reality Models and automata in Computation Theory
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The Pixie
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Member # 548
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posted 22. October 2003 08:00
Russell
quote:
Reality is that which contains all and only that which is real...
If our universe were to occupy a medium into which it could expand, the medium would be an even more basic form of reality than the universe itself. If the more basic form of reality were to occupy such a medium, the medium would be even more basic. A contradiction. Reality cannot be expanding in any external sense. Thus, the real universe inwardly creates its own scales of extension and duration. The reality principle also agrees with the background independence of general relativity i.e curvature is intrinsic, so there is no higher dimensional space that can serve as a fixed background. Since curvature is intrinsic to the manifold it is invariant.
Can you tell us exactly what you mean by universe? From what you have written it is not clear if you are considering the universe to be identical to reality, i.e. that which contains everything real, or if you consider the universe to be a very large container for galaxies, which is apparently expanding. Or are the making the assumption that these two things are the same?
I certainly agree that reality (as defined) cannot be measured in any external sense, and so to say externally it is expanding, contracting or or keeping constant size is meaningless.
The Pixie
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chimp
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posted 22. October 2003 09:10
Hello again Pixie, ![[Wink]](wink.gif) of course, the real universe is defined as the totality of all that exists.
Yes, we cannot be certain that the observable universe is expanding in any absolute sense. All motion is relative, such, that an expanding spacetime can also be explained as matter-energy contraction at the quantum scale. As the scientist Arthur Eddington explains,the theory an the expanding universe could also be called the theory of the shrinking atom.
One could define the universe as a sub region of a larger meta-space, but what contains the meta-space? It becomes an infinite regress unless the meta-space is defined as truly "infinite" in duration and extent but that creates another problem because it cannot give us finite[sensible] answers in the mathematical calculaions.
More problems and paradoxws are created by defining the universe as infinite, it seems.
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980815b.html
Of course the universe could be part of a multiverse, if the multiverse is defined as a resonating system, where the individual universes are at different frequency - wavelengths. All the universes would be "phase entangled" with each other...
[ 22. October 2003, 09:28: Message edited by: Russell E. Rierson ]
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Aliet Jacob
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posted 22. October 2003 09:28
Russel,
In the interest of an honest discussion, I think you will do best to respond to posts that address the assertions you have made, and avoid examination of my level of expertise.
In light of your recent post, do you know the difference (if any) between self-composition and self-inclusion in light of the CTMU?
Conspansion assumes three ideas that you have yet to explain:
1. There is no additional matter being created in some parts of the universe.
2. The universe has a static volume (expansion is illusory since its accompanied by a corresponding contraction)
3. There is a multiverse (with a static volume) and our universe is one just of the items expanding within it. If our universe is concentrically surrounded by a static mega universe (megaverse) such that while our universe expands, the free space within the megaverse contracts, you also need to explain why its one universe.
Notice that the first section of point 3., whichever way you wing it, is the tower of turtles (but good for Tegmarkian parallel universes), which is like ants in the pants of CTMU.
Are these three all correct or all wrong with regard to expansion? Can you point out which one among the three above is consistent with conspansive duality?
It would be good if, instead of posting chunks from Langan's articles, you offered your interpretation of them.
This may be my last post on this thread. Thanks for indulging me.
[ 22. October 2003, 09:34: Message edited by: Aliet Jacob ]
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chimp
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posted 23. October 2003 01:53
quote:
2. The universe has a static volume (expansion is illusory since its accompanied by a corresponding contraction)
The universe has no external measure. All relationships are intrinsic.
http://www.iomas.com/gina/ultrahiq/Mega-Society/NoesisMay/SupernovaCL.asp
quote:
As previously described, if the conspanding universe were projected in an internal plane, its evolution would look like ripples (infocognitive events) spreading outward on the surface of a pond, with new ripples starting in the intersects of their immediate ancestors. Just as in the pond, old ripples continue to spread outward in ever-deeper layers, carrying their virtual 0 diameters along with them. This is why we can collapse the past history of a cosmic particle by observing it in the present, and why, as surely as Newcomb’s demon, we can determine the past through regressive metric layers corresponding to a rising sequence of NeST strata leading to the stratum corresponding to the particle’s last determinant event. The deeper and farther back in time we regress, the higher and more comprehensive the level of NeST that we reach, until finally, like John Wheeler himself, we achieve “observer participation” in the highest, most parallelized level of NeST...the level corresponding to the very birth of reality.
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The Pixie
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posted 23. October 2003 08:42
Russell
Your earlier post appeared to be a stand-alone proof albeit taken from CTMU) that the universe was not expanding.
quote:
...of course, the real universe is defined as the totality of all that exists.
Yes, we cannot be certain that the observable universe is expanding in any absolute sense. All motion is relative, such, that an expanding spacetime can also be explained as matter-energy contraction at the quantum scale. As the scientist Arthur Eddington explains,the theory an the expanding universe could also be called the theory of the shrinking atom.
Are you saying that the "real universe" comprises everything that exists, and the "observable universe" is the big space astronomers look at that contains galaxies and is apparently expanding? That would be consistent with what I suggested in my last post, but somehow I suspect that you believe these two to be one and the same (so why label them differently), and this seems to me to be an unwarranted assumption.
Whether the universe is shrinking, expanding or remains constant is merely a point of view. And we might note that the intuitive point of view, the point of view of an internal observer such as you or I, and (I would suggest) the useful point of view, is that the universe is expanding.
quote:
One could define the universe as a sub region of a larger meta-space, but what contains the meta-space? It becomes an infinite regress unless the meta-space is defined as truly "infinite" in duration and extent but that creates another problem because it cannot give us finite[sensible] answers in the mathematical calculaions.
More problems and paradoxws are created by defining the universe as infinite, it seems.
I am afraid I do not follow the logic. If the sub-region is the "observable universe", why can the meta-space not be the "real universe", which is finite and comprises everything. I can see no need for this to be infinite in size, as long as the expansion of the "observable universe" is not infinite.
Why must the meta-space be contained in something else? You are happy to have the CTMU not contained in anything (I guess), why not the meta-space or "real universe"?
quote:
More problems and paradoxws are created by defining the universe as infinite, it seems.
I better say that I feel intuitively that the universe is finite, I am just trying to understand what your point is. Does the CTMU prove the universe is finite, or does it allow an infinite universe (as measured internally) to have a finite size (externally)? If the later (which appears to be what you are claiming) are the paradoxes you mentioned eliminated if we have a universe that is only infinite according to an internal metric?
Pixie
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Noel Rude
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posted 23. October 2003 08:56
Perhaps a naïve note from the linguist gallery wouldn't be too far off the wall, that is, if what y'all mean by language is what we mean by Language (Language with the capital L). I've yet to find time or take the time to digest Chris Langen's writings, but his coherent lines in these threads surely intrigue.
Language subsumes all other information systems, mathematics included (of course you'd expect a linguist to say that). Mathematics is a formalized system that issues from a subset of linguistic categories (laws of arithmetic, etc.) and is intolerant of ambiguities (which in natural language are typically resolved at the discourse level).
Mathematics has been developed/discovered by people that already possess language, but (as far as we know) no one beginning with only a knowledge of mathematics has ever invented/discovered language. All of math can be "read off" in language, but no one as yet has produced a formal system that captures everything in a natural language. Natural Language comes first, all of science follows.
It's counter-evolutionary. The output of Natural Language -- meaning our knowledge, our science -- evolves. Our knowledge flows out of our linguistic capabilities, but a limited logic never evolves into Natural Language. At least we have never seen this happen. It would be interesting to see how someone might develop a theory as to how it might happen.
An interesting point was made by Aliet Jacob -- "Horse + Horn = Unicorn" -- if there are parallel IT & BIT worlds, one of matter/energy and one of information, it is interesting that in the study of both we are driven to atomic theory. It would seem that, whereas there are an infinite number of real and imaginary things that we can encode with language, at some point there must be a finite number of fundamental meaning units. Logicians and linguists have had trouble developing a method for isolating and limiting these categories -- some linguists, however, have suggested that those categories that get grammaticalized across languages (tense, cause, hierarchy, individuation, etc. ... the list is finite) are precisely the same units of which all information is composed.
The categories that linguists are investigating extend beyond those found in the formal systems of the logicians and mathematicians -- this is especially true at the discourse level, and clause internally.
Logic-mathematics is concerned with propositions/functions and the relations that unite them -- beyond this linguists study the principles which give coherence to larger texts. Few scientific theories -- especially theories of everything -- can be stated formally without recourse to speech. It is only Natural Language that unites all our theories.
Logicians hardly mention the relationships that unite the arguments within a proposition - they are interested in the logical relations that exist between P1 and P2 but not those that exist between x, y, and z in P(x, y, z). The study of these relations -- called semantic roles -- has a distinguished pedigree in linguistics, from the Prague School to the California School and in the formalism of Relational Grammar. Information is chunked into minimal units (clauses/propositions) that encode events or states with up to three arguments. The verb names the event or state and establishes the semantic case roles of its arguments. Verbs have "valence" -- intransitive verbs have a valence of one (or zero), unitransitive verbs a valence of two, and ditransitive verbs a valence of three. The arguments implied in a verbs valence are called core (in Lucien Tesnière's model actant). Oblique (or circonstance) arguments are those relating to space, time and manner -- they can be appended to any clause but are not implicit in the meaning of the verb
The limit to a valence of three (no verbs have a valence beyond three) corresponds to the three core semantic roles -- Agent, Dative, and Theme. These are named 1, 2, and 3 in Relational Grammar so as not to prejudice their function as structural primitives.
The Theme is mere entity. It may or may not be affected or effected, but whether or not it is conscious this consciousness is not relevant to its role in the event or state. Consciousness is the relevant characteristic of the Dative (not everyone uses this term), and volition of the Agent -- it is a conscious cause.
Intransitive (valence 1) verbs lexicalize subjects of all three core semantic roles -- thus 'fall' and 'die' have Theme subjects, 'hurt' and 'be hungry' have Dative subjects, and 'come' and 'jump' have Agent subjects. Transitive (valence 2) verbs lexicalize any two core cases, i.e., EAT (Agent, Theme), SEE (Dative, Theme), EMBARRAS (Agent, Dative), and transitive (valence 3) verbs lexicalize all three core semantic roles, e.g., GIVE (Agent, Dative, Theme), SHOW (Agent, Dative, Theme), TEACH (Agent, Dative, Theme).
Additionally these semantic case roles enter into the following "accessibility" hierarchy:
In English this can be seen in the word order in (2) where where no grammatical morphology is needed. Change the order and extra morphology enters the picture.
- John (Agent) gave Mary (Dative) money (Theme)
The hierarchy above has to do with (among other things) the relative importance these case roles have in developing coherence in discourse.
Now -- of what relevance to this thread is all this?
Just that all our logico-mathematical formalisms ignore consciousness and volition, but that it is precisely these that are the most fundamental categories of Natural Language -- including the language (coherent or incoherent) in all the threads at Brainstorms.
[ 23. October 2003, 09:13: Message edited by: Noel Rude ]
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gedanken
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posted 23. October 2003 09:23
quote:
Language subsumes all other information systems
I disagree. I've seen some very effective communication by gesture and expression, with subtitles that are not easily (if at all) embedded in spoken or written language.
Now of course syntactic language has great power by its infinite number of potentially meaningful constructions. However in some circumstances, a gesture and expression can, so to speak, be worth a "1000 words", etc.
So is gesture and expression, without sound, "language"? If so, is observation of visual configuration of the real world "language", or feeling of shape by hand (even blindfolded)? Is a handshake "language"? Can language express all the information that can be transferred by such observations or senses? Can language completely describe information gained by sense of smell, taste? Each of these has been used as part of an “information system” by man an animal.
[ 23. October 2003, 09:28: Message edited by: gedanken ]
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Noel Rude
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posted 23. October 2003 11:48
Ged disagrees but asks some good questions. Linguists define language as a system for encoding complex information – gestures, smiles, tail wags, growls … these are cues to emotions, attitudes, feelings, but they cannot tell me that your father was from Latvia, that he survived the Holocaust and arrived in New York as a child refugee after the war, but nevertheless was robbed of his wallet and papers the day he arrived.
Gestures are auxiliary to language. They can be described as part of language but they are not Language. Intonation, for example, is most prototypically gestural. In writing, as in writing English, the intonation is missing – though Brainstorms lets us supplement our speech with an alternative, e.g., hmm (how do you insert those graemlins?). The writing preserves the language but loses its auxiliary intonation.
The question of perception (seeing, hearing, tasting, feeling) is tougher. Is perception information? And can language “completely” describe perceptions/sensations? We have words like red, sad, satisfied which name “qualia” that only another mind can appreciate. But is, say, the neural impulse traveling up the optic nerve information? How about the signal from an unmanned Mars explorer – is that information? What about a photograph? Is that information? Is a mere image of something information? Is the world itself information?
Well … I’d just say that we cannot define information without a proper theory of mind, and that language is the rule governed (propositional, syntactic, coherent) encoding of complex information.
[ 23. October 2003, 11:55: Message edited by: Noel Rude ]
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gedanken
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posted 23. October 2003 15:39
But Noel, you original statement to which I disagreed was:
quote:
Language subsumes all other information systems, mathematics included
(my emphasis.)
That "all" would seem to be important to the further points.
I would point out that the first versions of 'mathematics', like that of Archimedes, required observing of pictures, etc., and was not strictly "syntactic".
My issue is not if one takes all forms of communication and calls them "language", rather the claim that thereupon "language" can still be considered "syntactic".
(Now of course sign languages like "American Sign Language" could be said to be almost strictly syntactic in nature, I mean to have syntax as much as any language. I am still getting at the "all" aspect, can "all" communication be classified as "syntactic"? We of course have Godel's theorem problems when we start to define formal language representations of mathematics--do we get outside of these limitations without going outside of synatctic representation of communicated concept?)
[ 23. October 2003, 15:44: Message edited by: gedanken ]
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Noel Rude
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posted 23. October 2003 19:15
About to head for home so this will have to be brief. In the real world “all” tends to be a dangerous claim so I won’t make it. What I was getting at is that Natural Language is the basis – in our experience – for all logico-mathematic systems – computer, whatever. But you bring up an interesting point that would take some time to dissect. In my school (Typological-Functional ling) we see Pidgins (imperfect speech learned only by adults) as primarily non-syntactic – T. Givón labels this a “pragmatic mode” which he distinguishes from the “syntactic mode” used by native speakers of ordinary languages. But you have to understand that by “syntactic” he means automated, routinized behavior (in speech, writing, sign language) – he does not mean that at a deeper semantic level the information conveyed by the speakers of Pidgins is without rules.
For example, I mentioned Case Theory in the earlier post – the core case relations Agent, Dative, and Theme. In no language do these equate in a one to one relationship to grammatical form ("syntax"). Rather languages have what we call grammatical (or syntactic) relations, i.e., subject, object, indirect object (etc.). Why? Because the automated behavior we call “syntax” is mediating between semantic case roles (Agent, Dative, Theme) and coherence relations (Primary Topic, Secondary Topic, Nontopic).
But what I have meant to convey, in my simple-minded way (my “pragmatic mode”?), is that individual languages (French [French!?], Umatilla, Japanese, etc.), mathematics, computer language, all logic systems devised by us – all these draw upon something deeper we call Language which, at least for those in my school who still subscribe to universals, consists of a finite set of logico-linguistic categories. And then I personally – most linguists probably would not follow me here – believe that this is Platonic – that when we draw on Language we are not finding it in the neurons (rather we are imprinting it there) – we discover it in the same way that the mathematical Platonist says we discover mathematics. In this sense especially I think linguistics may have something to contribute to grand Theories of Everything that would want to consider information and design as fundamental.
Also there’s much to say about the distinction linguists make between the emotive, connotative side of language and the logical, denotative side. They’re both there. I would suggest that there is no logic without passion. I find I respect a passionate atheist more than a dispassionate “apathist” – as also the passionate IDists of which I’d like to count myself. Passion empowers logic – all the truly great scientists have been passionate folks. Just an added thought there to chew on.
And, yes, you bring up the question of how much logic can issue from pure reason apart from observation – who can answer that? I suspect that reason alone wouldn’t get very far without observation – there are those experiments where people are deprived of all sensory experience and it isn’t long and they go stark raving mad. Maybe this relates to passion – maybe passion and experience go hand in hand – maybe ... but I’ve gotta get out of here.
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Aliet Jacob
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posted 24. October 2003 04:46
I will attempt to be brief. I am frustrated by having my posts deleted. But I feel compelled to contribute as a thread starter.
Noel, your questions are valid and you make good points. But I think you delve too deep into linguistics.
quote:
But is, say, the neural impulse traveling up the optic nerve information?
No, its not information. It is data. It becomes information (processed data) when it reaches the brain.
If we interpret a nerve impulse from a shot leg before it reaches the spinal cord, all we will get is some (bio)chemical state.
If you are given a teardrop, can you tell whether its a tear of pain or whether its a tear of laughter?
No you cannot.
Because its data. You need something extra in order to process it and get information.
The entropy of the neural impulse, when removed from the subsystem or the context from which it was generated, is zero. I am using Shannon entropy which refers to the amount of information contained in a 'message'.
Within the system of course, a nerve impulse should have high entropy (few[er] bits used to encode the information). But experts in sub-optimal design perhaps would have a different view (since you talked about the optic nerve - there is information lost - blind spot, blood vessels etc).
In response to your question, the neural impulse is not information per se but is coded information (what I called data earleir). It has to be processed (by the brain) to obtain information.
This (the processing) can be done consciously or unconsciously (like when asleep and a pin is pressed onto a leg, many reflexively withdraw the leg without waking up, and snore on).
Let me mention something about language in CTMU context.
Langan uses Language equivocally.
In his definitions, he defines language in terms of computational theory and talks of transducers, automata, acceptors, state transitions etc.
In defining the Principle of Linguistic reducibility, he uses language in a linguistic sense (he defines reality as made up of expressions, perceptual states, relations, attributes and syntax).
The difference is profound. The semantic shifts and the equivocation between the mind, a perceptual state, an expression and language are difficult to notice and keep track of. And the difference between being stable and being logical, categorizations and 2V logic are hard to notice.
And in between them, he throws in cybernetics and we have input-output, feedback and what Markovian concepts.
Humans are not subject to language, but we 'generate' the syntax, the grammars, etc in order to make communication possible. Being the social animals that we have, and the emergence of societies, language is indispensible.
Automata are self-organizing systems and they generate grammars and are subject and are part of the syntax. There is not one without the other (ged/Rex and others can correct me if I am wrong).
Langan also clearly tangles up emergence and self-organization. Two distinct concepts. For example, sentience does not necessarily entail self-organization. Sentience can be an emergent property. And self-organization is not a result of being conscious or intelligent. Readings on random reality, based on Chaitin's randomness, plus Wolframs automata, make this idea quite clear.
To say the universe has a desire (its not possible to have a purpose without a desire) is an artifact of fallacy of composition (M=R) combined with a misapplication of several concepts.
Compare the following definition (Langan's) of grammar with Noel's in the context of dative, thematic and agentive.
Langan defines grammar thus:
quote:
a generative (or phrase structure) grammar G is a 4-tuple (N,T,P,σ ) consisting of (1) a finite set N of nonterminals; (2) a finite nonempty set T of terminals, with N ∩T=∅and N ∪T = A (the total alphabet of the grammar); (3) a finite set of productions P ⊂((N ∪T)*\T*) × (N ∪T)* consisting of nonterminal arguments and their possibly terminal transforms; and (4) an element σ of N called the starting symbol.
Langan also uses terms like 'raw data' in his CTMU paper which expose an incorrect understanding of information and data.
[ 24. October 2003, 05:07: Message edited by: Aliet Jacob ]
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chimp
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posted 24. October 2003 06:14
quote:
I am afraid I do not follow the logic. If the sub-region is the "observable universe", why can the meta-space not be the "real universe", which is finite and comprises everything. I can see no need for this to be infinite in size, as long as the expansion of the "observable universe" is not infinite.
Why must the meta-space be contained in something else? You are happy to have the CTMU not contained in anything (I guess), why not the meta-space or "real universe"?
By defining the universe as the largest possible set, we create a paradox, because the set of all sets is its own power set . Therefore, the cardinality of the set of all sets must be bigger than itself. We could explain the "meta space" as being truly infinite but that creates serious problems also. There is no outside to the universe, so your attempt at visualization of an outside will not work. We cannot Cartesian dualize an n-dimensional perendicular set of axes for an "outside" There is no way to imbedd the riemannian manifolds into a higher dimensional Euclidean space and still have a realistic model.
The CTMU resolves the set of all sets paradox by explaining the universe as a dynamic self including SCSPL language, via a two stage form of self containment. Descriptive/Topological. As Mr. Langan explains, the universe descriptively contains that which topologically contains the universe.
Read "Introduction to the CTMU":
http://www.megafoundation.org/CTMU.html
[ 24. October 2003, 06:18: Message edited by: Russell E. Rierson ]
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gedanken
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posted 24. October 2003 11:44
quote:
Automata are self-organizing systems and they generate grammars and are subject and are part of the syntax. There is not one without the other (ged/Rex and others can correct me if I am wrong).
This should certainly not be taken as a "correction"--but I found this to be an interesting view.
I have often used the data/information distinction as Aliet is using it and found this to be very important or useful, though common dictionary definitions tend to equivocate them.
That an automata is self-organizing is interesting in that automata are generally a model concept. Wolfram (if I understand) simply uses the automata concept (from modeling) and applies it as a model for portions of the real world. This is no different than has been done for "automata" for hundreds of years, though the meaning of "automata" has probably changed in subtle ways. The subtle change is a movement from use of automata as a concept of a system acting by classical physics rules, to a more generalized computational model for automata. Thus modern formal language theory, and theory of computation in general usurp and extend the original meaning of automata as a useful concept for agents involved in the ‘processing’ envisioned. (This is not, of course, in any way in conflict with the older classical physics basis, as a truly classical automation could process states without error and be mathematical isomorphic to the mathematically abstract automata with regard to inputs and outputs. What has changed from older notions of automata is probably the notion of the input/output relationship, along with a degree of abstraction of the concept of “state”.)
But as models, the term self-organizing is interesting since the definition of “self” is interesting. If a person proposes an automata as a model of a system that processes a formal language that he/she developed, how is the term “self” to be interpreted? I’m not suggesting any conflict—just that in use in analogic manner as seems to be rife in these discussions, that notion could easily be conflated in an unjustified manner.
One minor problem with “one without the other” is that there are useful automata that don’t take any input, yet generate outputs or exhibit interesting state behavior. Strictly that would be defining a null language, I suppose, but is a little unsettling.
Now associated with this view, I notice another interesting question. The optic nerve actually is (if I am not mistaken) involved in some actual processing of visual information. And furthermore the boundary between nerve as communication, and the brain as processing that “communication” is rather fuzzy, since processing already is taking place in the nerve connection. Furthermore the demarcation might not be totally clear in that process where “brain” starts and “nerve” leaves off.
That said, I still find the “data”/“Information” classification to be very useful, even if it leads to fuzzy demarcation problems. Part of the problem is precisely defining which is the “automata”, and which is the input-output system with its “data”, at some level of analysis. One could, in theory perhaps, model subsections of the brain as automata, with other sections providing “data” as input/output to that automata. Thus moving the boundary changes the definition of “data”, as “data” from one section is actually “information” as it becomes processed—yet could be viewed again as “data” when viewing that output.
Of course theories of how the brain actually operate are very very young science. And this will be a touchy subject around here, with many having ingrained philosophical positions that will cause them to deny the very meaningfulness of some of these views or points. (These issues may be bound up in interpreting the very terms of Mr. Langan’s document.)
Another problem comes into play when we go back to the older thought of an “automata” as a mechanism operating according to classical physics. But now keep the “mechanism” aspect, but advance to modern physics as the rule set for its operation. We no longer have the strictly linear input-output stream relationships that we could define in the modern abstract computational automata, simply because we are dealing with a three-dimensional object with modes of interacting with the environment that could potentially go beyond the simple linear “data” model. What does the interaction of multiple senses, simultaneously, and with those senses distributed as including vision and touch, actually mean as “data”? It becomes very difficult to model them as linear data streams (and by that I mean “linear” in the sense of the symbolic stream concept as though it was a “pipe” into the automata with strictly time ordered, or time line symbolic input or output.)
With this view of the automata going beyond classical physics, going beyond linear input/output, and going beyond strict symbolic decomposition of those inputs and outputs, the whole meaning of “information”, “data”, and associated discussion gets very interesting. Especially putting that in the context of “self-organizing” systems.
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Aliet Jacob
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posted 25. October 2003 08:08
Ged,
I am pressed for time and should offer a better response to your post but, as far as self-organizing systems, and being models alone go:
If you pour sand from a certain height, say two metres from the ground, the sand particles 'organize' themselves to form a cone with geometric precision.
Would you, from that experiment, conclude that the sand-particles are self-organizing?
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gedanken
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posted 25. October 2003 11:05
quote:
If you pour sand from a certain height, say two metres from the ground, the sand particles 'organize' themselves to form a cone with geometric precision.
Yes, I think that a reasonable view is that the cone is (at least in part) "self organizing".
I would point out that it depends upon environmental factors: Most notably a stable gravity, non-moving (relatively) target location, circular distribution of the "pour" source, and possibly stationarity in the distribution of particle sizes and shape factors.
Each of those variables can have an effect on the conic shape. Move the target linearly, and one gets an elongated form. Pour with a wide line distributed source, and once again the result is elongated. Moving the center of gravity is equivalent to moving the target. And while I think there is fair degree of insensitivity to the size per se of the particles, there are potentially roughness or cling factors of particle surface shape that change the slope, and would have to be evenly distributed to keep slope constant.
An equivalent case would be a particle field self-coalescing into a nearly spheroidal celestial body, by self-gravity based processes. I would consider these "self-organizing".
(And of course the "precision" in no case is better than roughly the granule size.)
[ 25. October 2003, 11:08: Message edited by: gedanken ]
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